Definition: a ratio of a volume of gas contained in a fluid to the total volume of fluid and gas is called as the “quality” and is designated as “Γ”.
                              Γ          =                                    V              1                        V                          ,                            (        1        )            where: V1—gas volume, V—total fluid & gas volume.
As follows from the definition, Γ falls within a range of 0 to 1. If Γ<0.5, the fluid is called as the “aerated fluid”; If Γ>0.5, the fluid is called as the “foam”. In this context, the “foam” term will be applied to the both cases. e.g., the foam quality of 0.9 means that the foam consists of 90% of gas and 10% of fluid.
Well cementing operations are required to provide a long-term stability of wells subjected to the formation pressure impact. Cementing is performed by injecting a cement slurry in a well through a pipe string; after that, the cement slurry is allowed to harden. In some cases, it's expedient to add some gas in the injected slurry to foam it up and to produce a lighter cement slurry; in so doing, it's important to correctly determine the quality “Γ” of the foamed cement slurry which is injected into the well. A proper determination of the foamed cement slurry quality is a major integral component of well-cementing activities, since this factor defines mechanical properties of cements and, therefore, the stability of well operation.
A formation fracturing process aims to enhance well productivity by forming or enlarging channels connecting the wellbore with the oil-bearing formation. This operation is achieved through the injection of a fracturing fluid into a well that passes through the underground rock beds, and the pressurized fracturing fluid injection into the underground rock beds. In this process, hard rocks start fracturing and one or several fractures either form, or enlarge. A fracturing fluid contains a propping agent (proppant) that occupies the fracture volume and prevent the fracture from closing. Therefore, an increased flow rate of oil, gas and water is provided. In some cases, foams or aerated fluids are applied as a fracturing fluid either to reduce a wellhead pressure, or to improve the removal of well fluids from the fractured area.
In the industry, the foam quality is generally determined by a direct measurement of the gas and fluid volumes in the foam; for this purpose, different methods and different tools are used. For example, this can be implemented by creating a special discharge contour en-route the foam flow direction, which comprises a chamber for gas separation from the foam, and a direct measurement of the gas volume, or a flowmeter-based measurement of a flow for each phase.
The U.S. Pat. No. 6,461,414 discloses a system for determination and control (if required) over the foam-forming process for a fluid that comes from the underground formation and passes through at least one gas-to-fluid separator where gas is removed from the formation fluid entering there from the underground formation. The system comprises a transducer for measuring a required parameter of a gas flow isolated from the formation fluid, which is a foam-forming indicator for the formation fluid. The system also includes a processor for processing of measured parameters as well as for the determination of the foam-formation ratio for the formation fluid.
The system additionally comprises a gas separator, i.e. a device for gas fraction separation from the gas stream to form a side-cut fraction; the said transducer measures the side-cut fraction parameters. A hollow shaft can be applied as the said separator. Either a densitometer, the device for measuring the density or optical density of a fluid in the gas stream, or a gas stream optical density transducer can be employed as the above-mentioned transducer.
To determine the foam-formation ratio, a gas sample is taken from the high pressure separator, and then either the sample density, or the oil flow rate are measured. After that, the relationship between the density or optical density and foam-formation ratio is established; the received signal is transmitted to a control device. The supply of at least one foam-foaming additive is controlled to effect control over the foam-forming process. Part of the flow should be sent to a bypass pipeline for forming a side flow to determine the foam quality in the flow; this deems to be a disadvantage of the system described above. The system does not allow the determination of the foam quality directly in the pipeline a fluid from the underground formation passes through. The application of a separator while defining the foam quality is a reason of high error occurrence.
The U.S. Pat. No. 5,470,749 discloses a method for continued measurement of a steam flow, which is employed for pressurized well injecting (with the aim to enhance oil production) at pressures which are much higher than the atmospheric pressure, and at a room temperature. This method calls for the following:                a) vapor of a known-quality (vapor volume to vapor & fluid volume ratio) is mixed with a surfactant—max 1% of vapor's fluid phase weight to form a stable foam with a quality which is on par with the vapor quality,        b) stable foam is directed through a non-conductive shielded capillary tube and a voltage drop between two electrodes located across the given tube length as well as a pressure drop across the same given tube length are measured,        c) the above-mention steps are repeated, using different quality vapors,        d) voltage drop vs. pressure drop diagram is plotted to define the foam quality (vapor volume to vapor & fluid volume ratio) for each vapor sample,        e) a sequence of vapor flow samples of unknown quality is removed and the steps a), b) are repeated for each sample to determine a ratio between the pressure drop and the pressure of a stable foam formed from the said vapor; thereafter, a temperature of the stable foam formed from the said vapor is measured to define the fluid-water and water-vapor phase volumes for the stable foam-forming flow,        f) quality of each sample of the stable foam is graphically determined at the step e) based on the relationship between the foam quality and voltage drop vs. pressure drop ratio, drawn at the step d), which is equal to the vapor quality,        g) vapor quality (vapor volume to foam volume ratio) obtained at the step f) for each sample is converted to the vapor quality (vapor weight per vapor & fluid weight), using a specific volume of the fluid-water and water-vapor phases determined at the step e).        
The disadvantage of this method is that, when it's required to define the foam quality, first it is necessary to converse vapor into a stable foam and then to take off part of the flow to the bypass pipeline, from which samples are then taken.
In case of the foam flow branching, e.g., during the formation hydraulic fracturing or well cementing activities, this method does not allow direct determination of the foam quality distribution. In this case, the quality is calculated theoretically or by using numerical simulations; for this purpose, quality data at accessible points of the flow (e.g., at the slurry injection point) or the injection diagram (or both) are specified. These measurements are impossible in industrial conditions, when monitoring of remote inaccessible sections (through which foam supply is arranged) is required.
It's possible to measure foam quality indirectly (i.e., not by measuring foam-forming gas & fluid volumes), using the monitoring of the foam physical properties.
As the nearest engineering approach, a method for the foam quality determination through a monitoring of the foam physical characteristics, which are dependent of the foam quality, can be considered. A speed of sound in the foam is one of the above-mentioned characteristics. The indicated sound speed vs. foam quality relationship is disclosed, e.g., in A. B. Wood's publication <<Textbook of Sound>>(London, 1964). The simplest example is a two-phase foam comprising a perfect gas and a non-viscous fluid. For this foam, sound speed is connected with the foam quality as follows:
                              C          fm          2                =                  N          ⁢                      p                                                            ρ                  fl                                ⁡                                  (                                      1                    -                    Γ                                    )                                            ⁢              Γ                                                          (        2        )            where: Cfm—speed of sound in foam, p—pressure, ρfl—fluid density, Γ—foam quality, N—polytrophic expansion coefficient (reference value, e.g., N=1 for isothermal process, N=1.4 for adiabatic process).
FIG. 1 shows the water foam sound speed relationship at p=10 MPa. It's also should be mentioned that a typical sound speed Cfm in foams is many-fold lower than the sound speed Clq in the reference fluid. This relationship is well-ascertained experimentally (e.g., ref. to K. Falk, J-S. Gudmundsson's publication <<Multiphase Pressure Pulses for Quick -Acting Valves: Offshore Testing>>, SPE 56526, or B. S. Gardiner <<Yield Stress measurements of aqueous foams in the dry limit >>, The journal of Rheology, 42(6), November/December, 1998). In S.W. Kieffer <<Sound Speed in Liquid-Gas mixtures: Water-Air and Water Steam >>(Journal of Geophysical Research, Volume 82, B20, 1977, pages 2895-2904), there is an example of the state-of-the-art theoretical analysis, which also confirms the applicability of Formula (1) for the foam quality determination.
For multi-phase multi-component fluid & gas mixtures, the sound speed vs. phase volume ratio relationship could either be measured in laboratory conditions (e.g., ref. to B. S. Gardiner's publication <<Yield Stress measurements of aqueous foams in the dry Limit>>), or calculated theoretically (e.g., ref. to B. Herzhaft's publication <<Rheology of Aqueous Foams: a Literature Review of some Experimental Works,>>Oil & Gas Science and Technology Rev. IFP, Vol. 54(1999), No. 5, pp. 587-596), which discloses a method for determining a mixture compressibility factor which predetermines the speed of sound in media.
Therefore, the foam quality can be defined by measuring a pressure and sound speed in the foam; a particular profile of the curve characterizing the relationship between the foam quality and pressure & sound speed can be found either analytically, or experimentally, or by numerical simulations. This relationship is hereinafter referred to as the <<chart>>.
Due to a strict sound speed vs. foam quality relationship, there is an opportunity of detecting the foam quality based on the results of integrated measurements of the sound speed and pressure in the foam. This opportunity becomes more attractive, in particular, owning to the emergence of innovative technologies for on-line well pressure measurement, e.g., by using optical fibers.
The sound speed vs. foam quality relationship is used in metering tools. A device for measuring the sound speed in binary gas mixtures to determine concentration variation for one component of the said mixture is known (e.g., ref. to Tinge J. T, et. al., <<Ultrasonic gas analyzer for high resolution determination of binary-gas composition,>>Journal of Physics E: Scientific Instruments, 19, 1986, pp. 953-956)).
A method of multi-phase fluid flow measurement for offshore wells is known (e.g., ref. to U.S. Pat. No. 5,741,978, Method for Determination of Flow Rate In a Fluid, J. S. Gudmundsson or to the publications of J. S. Gudmundsson et. al. <<Gas-Liquid Metering Using Pressure -Pulse Technology >>, SPE 56584and <<Two-Phase Flow Metering by Pressure Pulse Propagation>>, SPE 24778). All the above-mentioned methods are based on the specified sound speed vs. foam quality relationship.
However, known methods and devices do not allow to determine the quality of a foam, which is used in, e.g., well cementing or hydraulic fracturing of formations or in other industries, in the real time mode by conducting acoustic measurements.